Man with outstretched arms. 618 golden ratio constant

"Vitruvian Man" - a drawing by the Italian scientist Leonardo da Vinci, which he made for the book of the Roman architect Marcus Vitruvius Pollio, who lived in the first century BC, whose works in the form of a treatise "10 books on architecture" occupied the minds of scientists throughout Europe throughout many centuries.

Artist, scientist, engineer - Leonardo da Vinci

The painting "Vitruvian Man" was painted in 1492. It cannot be counted among paintings famous Florentine, such as "Lady with an Ermine", written in 1490, shortly before the creation of the "Vitruvian Man", or " The Last Supper", which was released in 1498. And even more so, comparison is impossible with the ingenious "La Gioconda", created in the period from 1505 to 1519.

canons

The drawing by Leonardo da Vinci reveals in detail the fundamental principles of the canonical proportions of a person, which in a certain way correlate with the architectural norms derived by Vitruvius. There are six in total:

Ordinatio - absolute order order or consistency. Vitruvius describes the general architectural principles, the formation of volume, the basis of dimensional relationships and proportions. Further, the scientist gives his famous triad: venustas - beauty, utilitas - benefit, firmitas - structural strength.
Dispositio - basis, local placement. A description of the principles of organization of space and the location of the object in three-dimensional format follows.
Eurythmia - determination of the most aesthetic proportions, the composition is being specified.
Symmetria - this category suggests the relationship of the architectural module with parts of the human body.
Decor - decorative and colorful, combined with order strictness in the arrangement of elements.
Distributio - a description of the methods that determine the economic side of the operation of the facility.

Geometry

The painting "Vitruvian Man" by Leonardo da Vinci became an illustration for the multi-volume treatise of Vitruvius, combining treatise and a work of art all in one. The figure shows a person in two guises: one position - with legs and arms spread apart - is inscribed in a circle, the second - with arms spread and legs brought together - is inscribed in a square. Moreover, both geometric figures organically correlate with each other, despite the fact that they are directly in contact at one lower point, and in six more - only indirectly.

"Vitruvian Man" - the most famous picture Leonardo da Vinci after La Gioconda. The value of a drawing is determined by engineering criteria. The human pose "legs together, arms apart" fits into geometric figure, which is called the "Square of the Ancients", and a person with spread legs and arms fits into a circle. At the same time, it is a regularity that the center of the figure in both cases falls on one point, which in everyday life is called the "navel", that is, the place where the umbilical cord leaves at the birth of a person.

Calculations

Here is what the "Vitruvian Man" looks like, the significance of which cannot be overestimated, from the point of view of mathematical analysis:

The distance from the tip of the middle finger to the base of the little finger is equal to the length of the palm.
The length of the foot is equal to the width of four palms.
Six palms are equal to the length of a cubit.
The height of a man of average height is 4 cubits or 24 hands.
A step is equal to one elbow and one palm.
Hands in a span equal to the height of a person.
The distance from the level of the hair on the head to the lower edge of the chin is 1/10 of the height.
The distance from the bottom line of the chin to the top of the head is 1/8 of the height.
The distance from the top of the head to the nipples is 1/4 of the height.
Shoulder width - 1/4 height.
The length from the elbow to the fingertips is 1/4 of the height.
The distance from the elbow to the armpit is 1/8 of the height.
Arm length - 2/5 height.
The distance from the nose to the lower edge of the chin is one third of the length of the face.
From the eyebrows to the hairline - a third of the length of the face.
Size auricles vertically is 1/3 of the length of the face.

Symbolism

The "Vitruvian Man" by Leonardo da Vinci is often used as a symbol of the symmetry of the human body.

A close examination of the drawing reveals four clearly marked positions of the human body and two dominant compositions. The first is the center of the figure located in a circle, this is the "navel" of a person, as a symbol of birth. The second - the center of the body, placed in a square, falls on the genitals and serves as a symbol of procreation.

"Vitruvian Man" is presented by Leonardo da Vinci as the personification of the universe and is considered the forerunner of the Italian Renaissance. Later, the French architect Corbusier successfully used the theory of proportions of the human body to create his own Modulor system, which is responsible for the convenience and ergonomics of housing. In 1952, the architect built a multi-storey residential building in Marseille, following the teachings of Vitruvius and the "Modulor" in its practical application.

Shroud

There is also an assumption that the drawing "Vitruvian Man" is an image of Christ on the holy shroud, which Leonardo da Vinci transferred to paper during the restoration of the relic. This version has the right to life, since it is known for certain that the keepers of the shroud with the image of Christ handed it over to the scientist for restoration.

Being impressed by the divine proportions appearing on the shrine, da Vinci created his masterpiece and thus placed man as the image of God in the center of the Universe. And today "Vitruvian Man", the meaning of the creation and existence of which goes far beyond artistic image, symbolizes man in the universe and is an example of ideal proportions for architecture.

Vitruvian Man is still the subject of close scrutiny. The image, created by the genius of Leonardo da Vinci, contains many mysteries and raises many questions.

One of the factors affecting the visual perception of a person is certain relationships between the components of the whole. But the Vitruvian Man is not only an image of the ideal proportions of the human body. The work of the legendary Leonardo da Vinci is filled with a deep philosophical, symbolic, spiritual meaning.

History of appearance

pencil drawing was made Italian master when studying the works of a citizen of Rome, the architect Mark Vitruvius. exact date no one knows the writing of these works, but they are usually dated to the first century BC. In one of the books of Vitruvius, in detail are described ideal proportions human body. However, the work does not contain any illustrations.

Before Leonardo da Vinci, many illustrators tried to translate the content of the notes into images, including the friend of the great master Giacomo Andrea da Ferrara. Documentary evidence is known that friends discussed among themselves the works of the Roman architect.

Known to everyone in modern times, the Vitruvian Man is very similar to Giacomo's drawing. However, the essence of the work of Leonardo da Vinci is completely different. This is not just an illustration of the text. It is both a scientific work and a work of art.

The union of the spiritual and the material

One of the obvious differences between Leonardo da Vinci's drawing and others is the position of a person, his place in a circle and a square. The image contains not one, but several figures at once. Moreover, when the pose changes, the center of the picture also shifts: it is either the center of the square (for a figure with legs brought together), or the center of a circle (for a person with outstretched legs and arms).

The reduced legs of the figure are on the side of the square, which is tangent to the circle. Researchers see in this the duality of the Vitruvian man as a divine, but still earthly being, close to material reality.

Another detail of the drawing shows how the artist distinguishes between the spiritual and material principles in a person: the measuring lines refer only to the figure inscribed in a square. A person inscribed in a circle, as a divine and spiritual being, is not related to various measures of measurement, and perhaps, according to Leonardo's plan, cannot be.

Mysteries of the Vitruvian Man

There is a version that the creation of a picture is related to work Italian artist over the Shroud of Jesus Christ. It was at this time that she was master of genius. He was engaged in the study and restoration of historical relics.

Researchers believe that the perfect proportions of the body of Christ inspired the master to embody them in the drawing. The Vitruvian Man is a depiction of the divine proportions of the human body.

Position male figure, its presence at the same time in the middle of the circle and in the middle of the square suggests that for the great Leonardo, man is the center of the Universe, the image of God, embodied in reality.

Vitruvian man in modern times is perceived as a symbol of the natural symmetry of the human body and the entire universe, material and spiritual, ideal and rational. The location of a human being simultaneously inside a circle and a square leads the viewer to an understanding of the inseparable connection between a person and the Universe, between his inner (spiritual) and surrounding (material) world.

Creating works of art is impossible without observing strict ratios and proportions. They do not appear from nowhere, they are created by nature itself. The Vitruvian Man by Leonardo da Vinci is one of the brightest illustrations of the laws of harmony to which the entire Universe is subject.

"Vitruvian Man" - a drawing made by Leonardo da Vinci around 1490-1492 as an illustration for a book dedicated to the works of Vitruvius. The figure is accompanied by explanatory inscriptions. It depicts the figure of a naked man in two superimposed positions: with arms outstretched to the sides, describing a circle and a square.

Drawing and text are sometimes referred to as canonical proportions. When examining the drawing, it can be seen that the combination of arms and legs actually amounts to four different postures. A pose with arms spread apart and legs not spread apart fits into a square (“square of the ancients”). On the other hand, a pose with arms and legs spread out to the sides fits into a circle. And although the center of the figure seems to move when changing positions, in fact the navel of the figure, which is its real center, remains motionless.

Vetruvio architetto mette nelle sue opera d"architettura che le misure dell"omo…"(The architect Vetruvius laid the dimensions of a person in his architecture ...) The following is a description of the relationship between various parts human body.

In the accompanying notes, Leonardo da Vinci indicated that the drawing was created to study the proportions of the (male) human body, as described in the treatises of the ancient Roman architect Vitruvius, who wrote the following about the human body:

“Nature ordered the following proportions in the structure of the human body: the length of four fingers is equal to the length of the palm, four palms are equal to the foot, six palms are one cubit, four cubits are the height of a person. Four cubits are equal to a step, and twenty-four palms are equal to the height of a man. If you spread your legs so that the distance between them is 1/14 of a human height, and raise your hands so that the middle fingers are at the level of the crown, then the central point of the body, equidistant from all limbs, will be your navel. The space between the legs apart and the floor forms an equilateral triangle. Length arms outstretched will be equal to growth. The distance from the roots of the hair to the tip of the chin is equal to one tenth of human height. The distance from the top of the chest to the top of the head is 1/6 of the height. The distance from the upper chest to the roots of the hair is 1/7. The distance from the nipples to the crown is exactly a quarter of the height. The greatest shoulder width is an eighth of the height. The distance from the elbow to the fingertips is 1/5 of the height, from the elbow to the armpit - 1/8. The length of the entire arm is 1/10 of the height. The beginning of the genitals is located just in the middle of the body. The foot is 1/7 of the height. The distance from the toe of the foot to the patella is equal to a quarter of the height, and the distance from the patella to the beginning of the genitals is also equal to a quarter of the height. The distance from the tip of the chin to the nose and from the roots of the hair to the eyebrows will be the same and, like the length of the ear, equal to 1/3 of the face.

The rediscovery of the mathematical proportions of the human body in the 15th century by Leonardo da Vinci and others was one of the great achievements that preceded the Italian Renaissance. The drawing itself is often used as an implicit symbol of the internal symmetry of the human body.

Art is inherent in the desire for harmony, proportion, harmony. We find them in the proportions of architecture and sculpture, in the arrangement of objects and figures, in the combination of colors in painting, in the alternation of rhymes and rhythm in poetry, in the sequence musical sounds. These properties are not invented by people. They reflect the properties of nature itself. One of the proportions is most often found in art. She was named " golden ratio". The golden ratio has been known since ancient times. So in book II of Euclid's "Beginnings" it is used in the construction of pentagons and decagons.

The term "golden ratio" was introduced by Leonardo da Vinci: "If human figure- the most perfect creation of the universe - we tie it with a belt and then measure the distance from the belt to the feet, then this value will refer to the distance from the same belt to the top of the head, as the entire height of a person relates to the length from the belt to the feet ... "

Indeed, in nature and the human body there are many proportional relationships close to what Leonardo da Vinci called the golden section. Although not embodying it exactly. By the way, the golden ratio, which is preferred in many cases, is not single relation visually perceived as beautiful. These include relationships such as 1:2, 1:3. They are close to the golden ratio. In any work of art, several unequal, but close to the golden section, parts give the impression of the development of forms, their dynamics, proportional complement to each other. In particular, the ratio based on the golden ratio is most common in the construction of monuments.

Is it possible to talk about the golden ratio in music? It is possible if you measure musical composition by the time of its execution. In music, the golden ratio reflects the features human perception temporary proportions. The point of the golden section serves as a guide for shaping (especially in short essays), often it has a climax. It may also be the most bright moment or the quietest, densest place in terms of texture or the highest pitch. But it also happens that a new musical theme appears at the point of the golden section.

Leonardo da Vinci

Vitruvian Man

The golden ratio in art

There is an opinion that a true creator does not create art himself, but allows God or energy (as you like) to direct the brush, merging into a single whole and totally turning into the mystery of creativity.

Little is known about Leonardo da Vinci as a person. There is much more information about him as a mystic, capable of uniting with the whole. His creations in various fields of knowledge and arts say more about him than he himself or those who knew him well could tell. The materials of his works that have come down to us testify to the disclosure of the fundamental principles of beauty by him.

The Vitruvian Man is an illustration of the works of the ancient Roman architect Vitruvius, made by Leonardo da Vinci around 1490-92 in his journal, along with explanations. The figure shows the figure of a naked man in two superimposed poses with arms and legs spread apart, inscribed in a circle and a square.

Combinations of arms and legs make up four poses. A pose with arms spread apart in two positions and legs not spread apart fits into a square, the so-called "Square of the Ancients". Two more poses with arms and legs spread out to the sides, fits into a circle. The center of the figure always remains fixed.

"Vetruvio architetto mette nelle sue opera d'architettura che le misure dell'omo..."“The architect Vetruvius laid the dimensions of man in his architecture ...”

The accompanying notes of Leonardo da Vinci explain that the drawing was created by him to study the proportions of the human body, as described in the treatises of the ancient Roman architect Vitruvius, who wrote the following about the human body:

“Nature disposed of the following proportions in the structure of the human body:
the length of four fingers is equal to the length of the palm,
four palms are equal to a foot,
six hands make one cubit,
four cubits is the height of a man.
Four cubits are equal to a step, and twenty-four palms are equal to the height of a man.
If you spread your legs so that the distance between them is 1/14 of a human height, and raise your hands so that the middle fingers are at the level of the crown, then the central point of the body, equidistant from all limbs, will be your navel.
The space between the legs apart and the floor forms an equilateral triangle.
The length of the outstretched arms will be equal to the height.
The distance from the roots of the hair to the tip of the chin is equal to one tenth of human height.
The distance from the top of the chest to the top of the head is 1/6 of the height.
The distance from the upper chest to the roots of the hair is 1/7.
The distance from the nipples to the crown is exactly a quarter of the height.
The greatest width of the shoulders is an eighth of the height.
The distance from the elbow to the fingertips is 1/5 of the height, from the elbow to the armpit is 1/8.
The length of the entire arm is 1/10 of the height.
The beginning of the genitals is located just in the middle of the body.
Foot - 1/7 of the height.
The distance from the toe of the foot to the patella is equal to a quarter of the height, and the distance from the patella to the beginning of the genitals is also equal to a quarter of the height.
The distance from the tip of the chin to the nose and from the roots of the hair to the eyebrows will be the same and, like the length of the ear, equal to 1/3 of the face.

Meaning of the Vitruvian Man

"Everything new is a well-forgotten old" - says famous saying. The “resurrection” of the mathematical proportions of the human body from antiquity, made by Leonardo da Vinci in the 15th century, became the foundation of the great achievements that preceded Italian Renaissance. Vitruvian man in itself is a symbol of internal symmetry and natural harmony of the human body.

Any divine manifestation, including art, is inherent in the desire for harmony, proportion, harmony - for such a harmonious state of being, which we used to call beauty. Being ourselves part of the universal energy of beauty, we unmistakably distinguish one from the other. Ugly immediately catches the eye.

We find beauty in the proportions of architecture and sculpture, in the arrangement of surrounding objects and forms, in the combination of colors in paintings, in the alternation of rhymes and rhythm in poetry, in the combinations, sequences and gravity of musical sounds.

In nature and the human body, there are many proportional harmonious relationships close to the golden ratio of Leonardo da Vinci. However, the golden ratio is not the only ratio visually perceived as beautiful. These include relationships such as 1:2, 1:3. They are also close to the golden ratio.

In any work of art, several unequal, but close to the golden section, parts give the impression of the development of forms, their dynamics, proportional complement to each other. This property is used everywhere and has long been called "canonical proportions".

Each person is able to distinguish the beautiful from the ugly. For example, if he sees a house or some other structure that is not sustained in the proportions of the golden section, then it immediately becomes obvious that "something is wrong with it." Something is embarrassing. This landmark of harmony and a sense of beauty is in everyone.

"All art strives to become music." (Walter Pater)

"The greatness of art is most clearly manifested in music." (Johann Wolfgang Goethe)

How to determine the presence of the golden ratio in something that does not have material forms, in such as music? How to "measure" a piece of music by its beauty?

In music, the golden ratio reflects the peculiarities of human perception of time proportions. The point of the golden section serves as a reference point in the time of the sound of the work and often the culmination falls on it. Or it can be the brightest accent or the quietest “kachum”, the densest and most instrumental sounding place or the highest pitch, or the place where the crescendo ends, the change of rhythm.

It often happens that a new musical theme appears at the point of the golden ratio.

And as Frank Zappa said, "Talking about music is like dancing about architecture."

Listen...

listen good beautiful music and realize your beauty. Let the music reflect the beauty of the golden ratio of your being. Let there be goosebumps!

Where the music begins, thoughts disappear, the observer and the awareness of beauty appear (unless, of course, you listen to music, and do not use it as white noise as a background).

And the next time you listen to music, pay attention to what you are doing: listening or thinking. Just think of Leonardo.

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